Definition:Heronian Mean
From ProofWiki
Definition
The Heronian mean of two numbers $x$ and $y$ is defined as:
- $\displaystyle H = \frac {x + \sqrt{xy} + y} 3$
It can also be defined as:
- $\displaystyle H = \frac 2 3 \left({\frac {x + y} 2}\right) + \frac 1 3 \sqrt {x y}$
Thus it is seen to be a weighted mean of their arithmetic mean and geometric mean.
Source of Name
This entry was named for Heron of Alexandria.
